Chapter 4 (Dorf & Svoboda)
Vocabulary & Concepts
 planar circuit
A circuit which may be drawn on a plane surface in such a way that no branch crosses over or under any other branch.
 reference node
A node in a circuit that is chosen to be the reference for all of the other nodes in the circuit. It is usually the ground node of a circuit or the node that has the most branches going into it.
 node voltage
The voltage of a node in a circuit with respect to a chosen reference node.
 mesh
A loop in a circuit that does not contain any other loops within it.
 mesh current
A clockwise current that flows only around the perimeter of a mesh in a planar circuit. A branch between meshes will have a current in it that is the algebraic sum of the two adjacent mesh currents.

Node Voltage Analysis
A method of circuit analysis using node voltages and KCL applied to all the non-reference nodes. This is usually best applied to circuits with more current sources than voltage sources.

Mesh Current Analysis
A method of circuit analysis using mesh currents and KVL applied to all the meshes. This is usually best applied to circuits with more voltage sources than current sources.
 supernode
A large node composed of two nodes and the voltage source (independent or dependent) in the branch between them.
 supermesh
A large mesh composed of two meshes and the current source (independent or dependent) in the branch between them.


Conductance Matrix
A symmetric matrix, G , of conductance values which results for resistive circuits that contain only independent current sources. If we apply Cramer’s Rule to the set of equations that result from applying KCL to all of the non-reference nodes in Node Voltage Analysis we get the matrix equation:
Gv = i s
Where:
 a
G -G ab
-G ac
the matrix G =
-G ab
 b
G -G bc
-G ac
-G bc
 c
G
 n
G ij
G is the sum of the conductances at node n is the sum of the conductances connecting nodes i and j.
the matrix v is the vector consisting of the N unknown node voltages:
v a v = v b

v
N
the matrix i is the vector consisting of the N current sources where i sn
is the sum of all the source currents entering the node n: i s
=
i
i
i s1 s2 sN


Resistance Matrix
A symmetric matrix, R , of resistance values which results for resistive circuits that contain only independent voltage sources. If we apply Cramer’s Rule to the set of equations that result from applying KVL to all of the meshes in Mesh Current Analysis we get the matrix equation:
Ri = v s
Where:
the matrix R =
-R ab
 b
R -R bc
 a
R -R ab
-R ac
-R ac
-R bc
 c
R

R n ij
R is the sum of the resistances in each mesh is the resistance common to meshes i and j.
the matrix i is the vector consisting of the N unknown mesh currents:
i a i = i b
i
N
the matrix v is the vector consisting of the N voltage sources where v sj
is the sum the sources in the j th mesh with the appropriate sign assigned to each source:
v s1 v s
= v
v s2 sN


Ideal -vs- Practical Voltage Source
An ideal voltage source is independent of the current through it.
A (more) practical voltage source is modeled by an ideal voltage source in series with a resistor. This more closely approximates “real” voltage sources.

Ideal -vs- Practical Current Source
An ideal current source is independent of the voltage across it.
A (more) practical current source is modeled by an ideal current source in parallel with a resistor. This more closely approximates
“real” current sources.

Source Transformations
Two sources are equivalent if they produce identical values of voltage and current when connected to identical values of a load resistance. An practical current source can be shown to be equivalent to a practical voltage source. Hence we can transform one into the other by a source transformation.

Maximum Power Transfer Theorem
This theorem says that for an independent voltage source in series with an internal resistance, R s
, maximum power is delivered to a load resistance, R
L
, when R s
= R
L
.
Alternatively, the theorem says that for an independent current source in parallel with an internal resistance, R s
, maximum power is delivered to a load resistance, R
L
, when R s
= R
L
.
 topology
A branch of geometry concerned with the properties of a geometric figure which are unchanged when the figure is twisted, bent, folded, stretched, squeezed or tied in knots, with the provision that no parts of the figure are to be cut or joined.

(linear) graph
A simplified circuit diagram showing the circuit elements as lines and the nodes as dots.
 tree
A set of branches which does not contain loops and connects every node to every other node in the circuit, although not necessarily directly. There can be more than one tree for a given circuit.
 cotree
The complement of a tree, i.e. the rest of the branches of the circuit once a tree has been defined. There can be more than one cotree for a given circuit.
 link
Any branch in the cotree.

General Nodal Analysis
Similar to Node Voltage Analysis, using trees and cotrees. Usually it results in fewer equations.

General Loop Analysis
Similar to Mesh Current Analysis, using trees and cotrees. Usually it results in fewer equations.